A108733 Expansion of (1+18*x)^(1/3).

1, 6, -36, 360, -4320, 57024, -798336, 11632896, -174493440, 2675566080, -41738830848, 660232415232, -10563718643712, 170644685783040, -2779070597038080, 45576757791424512, -752016503558504448, 12474626706088132608, -207910445101468876800, 3479764291698268569600

Offset: 0

Author

N. J. A. Sloane, Jun 22 2005

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..799

Programs

Mathematica

CoefficientList[Series[(1 + 18 x)^(1/3), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 21 2020 *)

Formula

G.f.: (1-18*x)^(1/3) = 1 + 6*x/(G(0)-6*x) where G(k)= k*(1-18*x) + 1+ 6*x + 6*x*(k+1)*(3*k+2)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Jul 06 2012

a(n) ~ -(-1)^n * 2^n * 3^(2*n-1) / (Gamma(2/3) * n^(4/3)). - Vaclav Kotesovec, Jun 16 2018

D-finite with recurrence: n*a(n) +6*(3*n-4)*a(n-1)=0. - R. J. Mathar, Jan 20 2020